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Full-Text Articles in Physical Sciences and Mathematics
The Existence And Quantum Approximation Of Optimal Pure State Ensembles, Ryan Thomas Mcgaha
The Existence And Quantum Approximation Of Optimal Pure State Ensembles, Ryan Thomas Mcgaha
Theses and Dissertations
In this manuscript we study entanglement measures defined via the convex roof construction. In the first chapter we build the notion of an entanglement measure from the ground up and discuss various issues that arise when trying to measure the amount of entanglement present in an arbitrary density operator. Through this introduction we will motivate the use of the convex roof construction. In the second chapter we will show that the infimum in the convex roof construction is achieved for a specific set of entanglement measures and provide canonical examples of such measures. We also describe LOCC operations via a …
A Development Of Transfer Entropy In Continuous-Time, Christopher David Edgar
A Development Of Transfer Entropy In Continuous-Time, Christopher David Edgar
Theses and Dissertations
The quantification of causal relationships between time series data is a fundamen- tal problem in fields including neuroscience, social networking, finance, and machine learning. Amongst the various means of measuring such relationships, information- theoretic approaches are a rapidly developing area in concert with other methods. One such approach is to make use of the notion of transfer entropy (TE). Broadly speaking, TE is an information-theoretic measure of information transfer between two stochastic processes. Schreiber’s 2001 definition of TE characterizes information transfer as an informational divergence between conditional probability mass func- tions. The original definition is native to discrete-time stochastic processes …
Dynamical Entropy Of Quantum Random Walks, Duncan Wright
Dynamical Entropy Of Quantum Random Walks, Duncan Wright
Theses and Dissertations
In this manuscript, we study discrete-time dynamics of systems that arise in physics and information theory, and the measure of disorder in these systems known as dy- namical entropy. The study of dynamics in classical systems is done from two distinct viewpoints: random walks and dynamical systems. Random walks are probabilistic in nature and are described by stochastic processes. On the other hand, dynami- cal systems are described algebraically and deterministic in nature. The measure of disorder from either viewpoint is known as dynamical entropy.
Entropy is an essential notion in physics and information theory. Motivated by the study of …